In a nutshell, Google changed the API for YouTube (they want everyone to sign in with a Google account), which the WD TV Live freaks out about, causing the reboot. WD are blaming Google but not explaining why a login error reboots the unit.

There’s no firmware solution yet but there is a workaround, which is to create a new YouTube/Google account.

Check the thread link above for a better idea of what the problem is, plus the right way to set up the new account (linking your old YouTube account to your Google account doesn’t work).